Best Known (129, 129+129, s)-Nets in Base 4
(129, 129+129, 130)-Net over F4 — Constructive and digital
Digital (129, 258, 130)-net over F4, using
- t-expansion [i] based on digital (105, 258, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(129, 129+129, 180)-Net over F4 — Digital
Digital (129, 258, 180)-net over F4, using
(129, 129+129, 2099)-Net in Base 4 — Upper bound on s
There is no (129, 258, 2100)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 257, 2100)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 54789 174324 855812 200766 083512 003900 061587 171910 294038 678300 134343 817340 941217 397129 875806 422353 534907 540908 210597 410679 406406 091944 324637 410141 912818 322720 > 4257 [i]